Can we use cryptography to protect data while simultaneously enabling computation over it? Such cryptosystems have the potential to enable all of the amazing benefits of cloud computing without forcing users to give up control over their private data. The breakthrough development of fully homomorphic encryption (FHE) took the first step in this direction by showing how to perform arbitrary computations over encrypted data, without revealing anything about the data itself. In this talk, I will survey some of my work that goes beyond FHE to enable computation over cryptographically protected data in many other scenarios. We will discuss Fully Homomorphic Signatures, Multi-Key FHE, Laconic Function Evaluation, and Program Obfuscation.